Financial Risk Manager Part 1
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The following data represents a sample of daily profit of a sales company for six weeks in a particular year.
| Week | Amount of the Profit($) |
|---|---|
| 1 | 3,800 |
| 2 | 2,800 |
| 3 | 2,700 |
| 4 | 9,900 |
| 5 | 2,600 |
| 6 | 4,300 |
What is the 75% quantile profit?
Other
Community
NNikitesh
A
4,000
B
4,234
C
4,050
D
4,654
Explanation:
Step-by-step explanation:
-
Sort the data in ascending order:
- 2,600 (Week 5)
- 2,700 (Week 3)
- 2,800 (Week 2)
- 3,800 (Week 1)
- 4,300 (Week 6)
- 9,900 (Week 4)
-
Calculate the position for the 75th percentile:
- Formula: α × n = 0.75 × 6 = 4.5
- Where α = 0.75 (75th percentile) and n = 6 (number of observations)
-
Determine the value at position 4.5:
- Since 4.5 is not an integer, we need to take the average of the values at positions 4 and 5
- Position 4: 3,800 (Week 1)
- Position 5: 4,300 (Week 6)
- Average = (3,800 + 4,300) ÷ 2 = 8,100 ÷ 2 = 4,050
Key concept: For quantile/percentile calculation when the position is not an integer, we interpolate between the two nearest data points. The 75th percentile represents the value below which 75% of the observations fall.
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